Serving advanced learners (and their teachers) since 2012.

CCSS Math Standard: 3.OA.9

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Broken Calculator: Multiplication Cross Product Gr 3-5
Broken Calculator: 2-Digit Addition Gr 1-4
Broken Calculator: 2-Digit Subtraction Gr 1-4
Factors and Codes: First Names (Episode 2)
Factors and Codes: First Names (Episode 2)
Scrambled up somewhere in 161,000 is a first name. Can you find it!?
Gr 4
Factors and Codes (Episode 1)
Factors and Codes (Episode 1)
Let’s use factors to encode and decode words.
Gr 4
Crossing Every Bridge Exactly Once (aka Eulerian Paths)
Crossing Every Bridge Exactly Once (aka Eulerian Paths)
How can you cross each bridge in this city exactly once?
Gr 2-4
Math Curiosity: Magic Triangles
Math Curiosity: Magic Triangles
Can you make each side of this triangle add up to 9 using the digits 1-6?
Gr 2-8
How Many Will There Be? Chip Off The Block
How Many Will There Be? Chip Off The Block
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
How Many Will There Be? Earthworm
How Many Will There Be? Earthworm
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
How Many Will There Be? Courtyard
How Many Will There Be? Courtyard
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
How Many Will There Be? Checkerboard
How Many Will There Be? Checkerboard
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
How Many Will There Be? Crosses
How Many Will There Be? Crosses
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
How Many Will There Be? Squares in Squares
How Many Will There Be? Squares in Squares
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
What’s the Pattern? Fraction Addition
What’s the Pattern? Fraction Addition
Can your students figure out how to add fractions by looking for a pattern?
Gr 5
Find The Pattern: Multiply Fractions
Find The Pattern: Multiply Fractions
What if you set the stage for students to discover how to multiply fractions?
Gr 5
Fizz Buzz: A Counting and Divisibility Game
Fizz Buzz: A Counting and Divisibility Game
Ready for a tricky counting and divisibility game?
Gr 3-6
How Many Ways: Fraction Subtraction 234
How Many Ways: Fraction Subtraction 234
How many different ways can you make this fraction subtraction statement true using only the digits one through nine?
Gr 4-5
How Many Ways: Fractions Divide Equals 2/3
How Many Ways: Fractions Divide Equals 2/3
One equation. Digits one through nine. How many ways can you make it work?
Gr 5-6
How Many Ways: Fractions Multiply 2/3
How Many Ways: Fractions Multiply 2/3
How many different ways can you make this fraction multiplication statement true using only the digits one through nine?
Gr 5-6
How Many Ways: Divide Fractions Equal 1/4
How Many Ways: Divide Fractions Equal 1/4
How many different ways can you make this fraction division math statement true using only the digits one through nine?
Gr 5-6
How Many Ways: Multiply Fractions Equal 1/4
How Many Ways: Multiply Fractions Equal 1/4
One equation. Digits one through nine. How many ways can you make it work?
Gr 5-6
How Many Ways: Fraction Subtraction Equals 1/2
How Many Ways: Fraction Subtraction Equals 1/2
How many different ways can you make this math statement true using only the digits one through nine?
Gr 4-5
How Many Will There Be? Pyramids
How Many Will There Be? Pyramids
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
How Many Will There Be? Sliced Circles
How Many Will There Be? Sliced Circles
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
How Many Will There Be? Xs and Os
How Many Will There Be? Xs and Os
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
How Many Will There Be? Desks
How Many Will There Be? Desks
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
How Many Will There Be? Stairs
How Many Will There Be? Stairs
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
Gr 4-7
How Many Will There Be? Flowers
How Many Will There Be? Flowers
These flowers sure are getting bigger faster! How large will they be in step 10? What about step 50?
Gr 4-7
Game: Number Scrabble
Game: Number Scrabble
What if we played Tic-Tac-Toe with numbers and instead of three-in-a-row, we add up to 15? Well… then we’d have Number Scrabble!
Gr 1-6
Addition: 3 Digits Plus 2 Digits (Multiple Solutions)
Addition: 3 Digits Plus 2 Digits (Multiple Solutions)
Typical practice problems don’t move students up Bloom’s Taxonomy. With this framework, you’ll see kids stop and really think about how to approach multi-digit addition.
Gr 3-6
How Many Will There Be? Triangles Within Triangles
How Many Will There Be? Triangles Within Triangles
A triangle splits and splits and splits again. How many will there be in step 20?
Gr 4-7
Math Curiosity: Klauber’s Triangle
Math Curiosity: Klauber’s Triangle
In 1932, a leading authority on rattlesnakes, Laurence Klauber, discovered a startling pattern within a triangle of primes.
Gr 2-8
Math Curiosity: Ulam Spiral
Math Curiosity: Ulam Spiral
What if we make a huge spiral of numbers and then highlight only the primes? Well, a bunch of weird patterns show up!
Gr 1-4
Math Curiosity: A Pattern Packed Triangle
Math Curiosity: A Pattern Packed Triangle
Pascal’s pattern-packed triangle is a potent puzzle for pupils to ponder.
Gr 4-5
Math Curiosity: Goldbach’s Conjecture
Math Curiosity: Goldbach’s Conjecture
Can any even number be written as the sum of two primes? Goldbach thought so, but we haven’t proven it… yet!
Gr 1-5
Evens and Odds – Addition and Subtraction
Evens and Odds – Addition and Subtraction
When we’re adding and subtracting, do evens make odds into evens? Do odds make evens odd? Which one has… more power!?
Gr 3-4
Create Your Own Operation
Create Your Own Operation
The commutative and associative properties are a whole lot more interesting when you apply them to a mathematical operation that you created!
Gr 3-4
Parentheses: How big of a change can they make!?
Parentheses: How big of a change can they make!?
Two tiny parentheses. One expression. How big of a change can they make? Bigger than you think.
Gr 3-8
How Many Ways: Fraction Equivalence
How Many Ways: Fraction Equivalence
How many different ways can you make this math statement true using only the digits one through nine?
Gr 3-5
How Many Ways: Times Equals Minus
How Many Ways: Times Equals Minus
How many different ways can you make this math statement true using only the digits one through nine?
Gr 3-5
How Many Ways: Times Equals Times
How Many Ways: Times Equals Times
How many different ways can you make this math statement true using only the digits one through nine?
Gr 3-5
How Many Ways: Order of Operations 1
How Many Ways: Order of Operations 1
How many different ways can you make this math statement true using only the digits one through nine?
Gr 5-6
How Many Ways: 2 Digit ÷ 1 Digit = 1 Digit
How Many Ways: 2 Digit ÷ 1 Digit = 1 Digit
How many different ways can you make this math statement true using only the digits one through nine?
Gr 3-4
Same Perimeter, Different Area For Rectangles
Same Perimeter, Different Area For Rectangles
Can two rectangles have the same perimeter but… different areas!?
Gr 3-4
Undoing Multiplication With Division
Undoing Multiplication With Division
Multiplication and division, natural foes, are constantly seeking to undo each other. Students will attempt to reverse the effects of multiplication by dividing once, twice, or even thrice!
Gr 3-4
Exponents – How Low Can They Go?
Exponents – How Low Can They Go?
Using exponent patterns, can students predict what the 0th power will be?
Gr 3-8
Calculators, Patterns, and Multiplying By Decimals
Calculators, Patterns, and Multiplying By Decimals
Before teaching students the procedure for multiplying with decimals, how much can they intuitively glean from a structured play session with calculators?
Gr 5
Math Curiosity: Four Squares
Math Curiosity: Four Squares
Every positive integer can be written as the sum of (at most) four perfect squares!
Gr 1, 2, 3, 4, 8
Math Curiosity: Magic Squares
Math Curiosity: Magic Squares
Imagine a 3×3 square in which every row, column, and diagonal have the same sum. That’s a magic square!
Gr 1-4
Math Curiosity: Odds & Squares
Math Curiosity: Odds & Squares
Why does the sum of the first 5 odds also equal 5 squared?
Gr 1-4
Doubling Dollars
Doubling Dollars
Say you have a dollar. Say you can double that dollar each day: $1, $2, $4, and so on. How long will it take to reach… one million dollars? Not as long as you might think!
Gr 3-6
Math Curiosity: Waring’s Conjecture
Math Curiosity: Waring’s Conjecture
So, can you write every odd (greater than 3) as the sum of three primes?
Math Curiosity: Primes and Squares
Math Curiosity: Primes and Squares
Can any perfect square be written as the sum of two primes?
Gr 2-4
Math Curiosity: Legendre’s Conjecture
Math Curiosity: Legendre’s Conjecture
It seems like there’s always a prime number between two perfect squares… but is this always the case!?
Gr 3-6
Math Curiosity: Finding Primes
Math Curiosity: Finding Primes
Prime numbers are unpredictable! How can we possibly find them all? An Ancient Greek mathematician found one way!
Gr 1, 2, 3, 4, 6
Math Curiosity: Twin Primes
Math Curiosity: Twin Primes
What do you call two prime numbers who are very close together?
Gr 3-5
Math Curiosity: Palindromic Number Conjecture
Math Curiosity: Palindromic Number Conjecture
Using this one weird trick, it seems that you can turn any number into a palindrome!
Gr 1-4
The Game of 100
The Game of 100
Who can get to 100 first in this simple, but delightful, math game?
Gr 2-7
Math Curiosity: Collatz Conjecture
Math Curiosity: Collatz Conjecture
The Collatz Conjecture: start with any number and get to 1 using just two rules. It seems to always work…
Gr 1-5